ТЕПЛОВАЯ ЭНЕРГИЯ ДИССОЦИАЦИИ И ОСНОВН ОЕ СОСТОЯНИЕF 2 + -ЦЕНТРОВ

+ - , , g - . , . .F ₂ ⁺ -. .     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

A borel-weil-bott approach to representations of sl q (2, ℂ)

We use a quite concrete and simple realization of sl _q (2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme ¹ II ^1* as the counterpart of the standard ¹ = Sl(2, )/B.     

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

Power law growth for the resistance in the Fibonacci model

Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n) (n),n,l ²(),, wherev(n)=[(n+1)]–[n],[x] denoting the integer part ofx and the golden mean , give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.     

The third-order electric susceptibilities of NaCl and KCl monocrystals

The dispersion of the third-order electric susceptibilities(; , , –) and(; , 0, 0) of NaCl and KCl monocrystals has been calculated by means of experimental data on the electro-optic Kerr effect. The result has been obtained by using semi-classical models of anharmonic oscillators. An ionic contribution to the electro-optic coefficients has been presented. From the result obtained it follows that the third-order electric susceptibilities are of the order of 10^–22 m² V^–2.     

ЭЛЕКТРОПРОВОД НОСТЬ И ТЕРМОЗЛЕКТРОДВИЖУ ЩАЯ СИЛА СЕРОГО ОЛОВА

, , , . .     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

ССЛЕДОВАНИЕ РАСПАДА Dy155 → Tb155

The gamma-spectrum and coincidences of gamma-rays appearing in Dy¹⁵⁵ Tb¹⁵⁵ decay have been measured with the aid of a scintillation gamma-spectrometer. The Dy¹⁵⁵ source has been obtained by a repeated chromatographic separation from Ho fraction produced by a spallations reaction Ta+p(E _p=660 MeV). Dy¹⁵⁵ appears as a decay product of Ho¹⁵⁵ (T _1/2= =45 min). In the gamma-spectrum new transitions in the energy range of 1170–2000 keV have been observed. As a result of- coincidence measurements we get a new energy level (1820±15 keV) of Tb¹⁵⁵.

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, Dy¹⁵⁵ . . .     

Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

AN EXTENSION OF “POPPER'S EXPERIMENT” CAN TEST INTERPRETATIONS OF QUANTUM MECHANICS

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics—namely that the state of a particle is merely an expression of what is known about the system—is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called Extension step 1)—which fully serves its original purpose—is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the many-worlds interpretation (MWI) is correct are shown to be identical. Only after a further modification (called Extension step 2) (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because what is known by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus—within the CI—for H they are known not to exist. Yet H can infer their existence by studying the evolution of the ion.     

Approximate ground state in a model with spontaneous symmetry breakdown

The spontaneous symmetry breakdown is treated by means of a variational approach. Use is made of coherent states of Glauber and of pairing states of BCS-type as the translationally invariant vacuum states for the discussion of the real scalar field ⁴ withm ₀ ² 0. The first type of trial states reproduces the usual approach to spontaneous symmetry breakdown (-) in the tree approximation (which is possible only form ₀ ² <0), while the second type of trial states offers the possibility of spontaneous symmetry breakdown even form ₀ ² =0.     

Physical properties of some McVittie metrics

A class of McVittie's new nonquadratic solutions is investigated in some detail with regard to its physical properties. It is found that decreasing pressure and density are not compatible with center regularity for these perfect fluid spheres. It is further seen that for gaseous spheres (i.e., the density drops to zero at the outer boundary of the sphere together with the pressurep) oscillatory motions arenot possible. For these gaseous models the pressure and the density are both positive inside the outer surface, and their respective gradients are negative. For the outer gaseous shells models are constructed where for a certain time interval the pressure is increasing for contracting models. Without any restriction with respect to time, for these shell models it found that the density is increasing for contracting models, and the adiabatic speed of sound is less than the speed of light. It is also found that the trace of the energy-momentum tensor is positive, the total mass is negative, and for collapsing shells the rate of change of circumference as measured by an observer riding on the shell is an increasing function of time. However, all these models have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate.     

A solution spectrum of the nonlinear Schrödinger equation. II

It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = _k,A _k (coshkx) ^–k and = _k B _k (coshkx) ^–k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure = _k=0 A _k(cosh kx)^–k–1/2and = _k=0 B_k(cosh kx)^–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum.